1. Field
This application relates to systems and methods for measuring geometry parameters with a single image, specifically with a known size reference object whose thickness can not be ignored in the single image.
2. Prior Art
People suddenly want to measure something in sight, but they haven't a ruler. Even in case a ruler is at hand, the thing to be measured may be in a position where it is difficult to put a ruler near it. In modern world, the number of people who take a camera device (such as mobile phone with digital camera or film camera) is by far larger than the number of people who take a ruler. If it can be seen, an image can be taken with the camera device.
So various measuring methods based on images had been developed. If 4 corresponding point pairs in two projection planes of the same object are known, a homography matrix can be determined. See the famous paper “A computer algorithm for reconstructing a scene from two projections”, H. C. Longuet-Higgins, Nature, vol. 293, pp. 133-135, Sept 1981. With this homography matrix and its inverse matrix, any point in the two planes can be calculated from one plane into the other plane and vice versa. The homography matrix is also known as fundamental matrix.
There are various algorithms (e.g., Normalized Direct Linear Transformation, Approximate Calibration and so on) to solve the homography matrix from 4 or more point pairs. For Approximate Calibration algorithm, See the paper “Navigation using affine structure from motion”, P. A. Beardsley, A. Zisserman, and D. W. Murray, Computer Vision—ECCV '94, Volume II, LN CS-Series Vol. 801, pp. 85-96, 1994. The Normalized Direct Linear Transformation (normalized DLT) algorithm is based on singular value decomposition (SVD) and the normalization process makes the input point data to be invariant with respect to arbitrary choices of the scale and coordinate changes. See the 4th chapter of the book “Multiple View Geometry in Computer Vision, 2nd Edition”, Richard Hartley and Andrew Zisserman, Cambridge University Press, 2003. A plane measurement device had been described at 1997 by A. Criminisi, I. Reid and A. Zisserman in the webpage of http://www.robots.ox.ac.uk/˜vgg/presentations/bmvs97/criminispaper/, in that webpage, a window's width is computed with a reference covering several other windows.
The current plane measuring method consists of 3 steps. First step is to take a image of the whole scenario, second step is to measure some reference object in the scenario with other measuring method (e.g., real ruler or laser scan) to get the metric data of the reference object and identify 4 point pairs in the image, third step is to compute the homography matrix and the length of line in the image.
The dependency of other measuring methods in second step makes it less useful. The current methods and systems also ignore the thickness of the real reference object, so the ignorance causes inaccuracy of the result if thickness can not be ignored actually.
Some mobile application (such as RulerPhone) uses credit/debit card as a reference object, because the credit/debit card's size is known without measuring, the dependency on other measuring methods is removed, but it had not deal with the perspective at the time of this application. See its website at http://benkamens.com/rulerphone.
If a geometry equation in Cartesian coordinates is already known with the unknown geometry parameters, enough independent points can determine the geometry parameters for the geometry equation. In http://mathworld.wolfram.com/Circle.html, if 3 valid points in the circle are provided, the geometry parameters (a.k.a., center and radius) of the circle can be determined. In http://mathforum.org/library/drmath/view/51735.html, if 5 valid points in the ellipse are provided, the center, axes and orientation can be determined.
When the geometry parameters are represented with real world metric values, calculating geometry parameters is considered as measuring geometry parameters because the geometry parameters have practical meanings.